Finding Optimal Formulae for Bilinear Maps

  • Razvan Barbulescu
  • Jérémie Detrey
  • Nicolas Estibals
  • Paul Zimmermann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7369)


We describe a unified framework to search for optimal formulae evaluating bilinear or quadratic maps. This framework applies to polynomial multiplication and squaring, finite field arithmetic, matrix multiplication, etc. We then propose a new algorithm to solve problems in this unified framework. With an implementation of this algorithm, we prove the optimality of various published upper bounds, and find improved upper bounds.


optimal algorithms polynomial multiplication and squaring finite field arithmetic tensor rank bilinear map bilinear rank 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Razvan Barbulescu
    • 1
  • Jérémie Detrey
    • 1
  • Nicolas Estibals
    • 1
  • Paul Zimmermann
    • 1
  1. 1.CARAMEL project-teamLORIA, Université de Lorraine / INRIA / CNRSVandoeuvre-lés-Nancy CedexFrance

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